Finite automata for caching in matrix product algorithms

A diagram is introduced for visualizing matrix product states which makes transparent a connection between matrix product factorizations of states and operators, and complex weighted finite state automata. It is then shown how one can proceed in the opposite direction: writing an automaton that ``generates'' an operator gives one an immediate matrix product factorization of it. Matrix product factorizations have the advantage of reducing the cost of computing expectation values by facilitating caching of intermediate calculations. Thus our connection to complex weighted finite state automata yields insight into what allows for efficient caching in matrix product algorithms. Finally, these techniques are generalized to the case of multiple dimensions.Comment: 18 pages, 19 figures, LaTeX; numerous improvements have been made to the manuscript in response to referee feedbac

Strontium and neodymium isotopic variations in early Archean gneisses affected by middle to late Archean high-grade metamorphic processes: West Greenland and Labrador

Relicts of continental crust formed more than 3400 Ma ago are preserved fortuitously in most cratons. The cratons provide the most direct information about crust and mantle evolutionary processes during the first billion years of Earth history. In view of their polymetamorphic character, these terrains are commonly affected by subsequent tectonothermal events. Hence, their isotope systematics may be severely disturbed as a result of bulk chemical change or local isotopic homogenization. This leads to equivocal age and source information for different components within these terrains. The Sr and Nd isotopic data are presented for early Archean gneisses from the North Atlantic Craton in west Greenland and northern Labrador which were affected by younger metamorphic events

The Multi-Component Nature of the Vela Pulsar Nonthermal X-ray Spectrum

We report on our analysis of a 274 ks observation of the Vela pulsar with the Rossi X-Ray Timing Explorer (RXTE). The double-peaked, pulsed emission at 2 - 30 keV, which we had previously detected during a 93 ks observation, is confirmed with much improved statistics. There is now clear evidence, both in the spectrum and the light curve, that the emission in the RXTE band is a blend of two separate non-thermal components. The spectrum of the harder component connects smoothly with the OSSE, COMPTEL and EGRET spectrum and the peaks in the light curve are in phase coincidence with those of the high-energy light curve. The spectrum of the softer component is consistent with an extrapolation to the pulsed optical flux, and the second RXTE pulse is in phase coincidence with the second optical peak. In addition, we see a peak in the 2-8 keV RXTE pulse profile at the radio phase.Comment: 12 pages, 3 figures, accepted for publication in Astrophysical Journa

Pacing Profiles in Competitive Track Races: Regulation of Exercise Intensity is related to Cognitive Ability

Pacing has been defined as the goal-directed regulation of exercise intensity over an exercise bout, in which athletes need to decide how and when to invest their energy. The purpose of this study was to explore if the regulation of exercise intensity during competitive track races is different between runners with and without intellectual impairment, which is characterized by significant limitations in intellectual functioning (IQ ≤ 75) and adaptive behavioral deficits, diagnosed before the age of 18. The samples included elite runners with intellectual impairment (N = 36) and a comparison group of world class runners without impairment (N = 39), of which 47 were 400 m runners (all male) and 28 were 1500 m-runners (15 male and 13 female). Pacing was analyzed by means of 100 m split times (for 400 m races) and 200 m split times (for 1500 m races). Based on the split times, the average velocity was calculated for four segments of the races. Velocity fluctuations were defined as the differences in velocity between consecutive race segments. A mixed model ANOVA revealed significant differences in pacing profiles between runners with and without intellectual impairment (p < 0.05). Maximal velocity of elite 400 m runners with intellectual impairment in the first race segment (7.9 ± 0.3 m/s) was well below the top-velocity reached by world level 400 m runners without intellectual impairment (8.9 ± 0.2 m/s), and their overall pace was slower (F = 120.7, p < 0.05). In addition, both groups followed a different pacing profile and inter-individual differences in pacing profiles were larger, with differences most pronounced for 1500 m races. Whereas, male 1500 m-runners without intellectual impairment reached a high velocity in the first 100 m (7.2 ± 0.1 m/s), slowly decelerated in the second race segment (−0.6 ± 0.1 m/s), and finished with an end sprint (+0.9 ± 0.1 m/s); the 1500 m runners with intellectual impairment started slower (6.1 ± 0.3 m/s), accelerated in the second segment (+0.2 ± 0.7 m/s), and then slowly decreased until the finish (F = 6.8, p < 0.05). Our findings support the hypothesis that runners with intellectual impairment have difficulties to efficiently self-regulate their exercise intensity. Their limited cognitive resources may constrain the successful integration of appropriate pacing strategies during competitive races

Warren McCulloch and the British cyberneticians

Warren McCulloch was a significant influence on a number of British cyberneticians, as some British pioneers in this area were on him. He interacted regularly with most of the main figures on the British cybernetics scene, forming close friendships and collaborations with several, as well as mentoring others. Many of these interactions stemmed from a 1949 visit to London during which he gave the opening talk at the inaugural meeting of the Ratio Club, a gathering of brilliant, mainly young, British scientists working in areas related to cybernetics. This paper traces some of these relationships and interaction

The matrix product representations for all valence bond states

We introduce a simple representation for irreducible spherical tensor operators of the rotation group of arbitrary integer or half integer rank and use these tensor operators to construct matrix product states corresponding to all the variety of valence-bond states proposed in the Affleck-Kennedy-Lieb-Tasaki (AKLT) construction. These include the fully dimerized states of arbitrary spins, with uniform or alternating patterns of spins, which are ground states of Hamiltonians with nearest and next-nearest neighbor interactions, and the partially dimerized or AKLT/VBS (Valence Bond Solid) states, which are constructed from them by projection. The latter states are translation-invariant ground states of Hamiltonians with nearest-neighbor interactions.Comment: 24 pages, references added, the version which appears in the journa